System and method for improving stability of drilling tools

ABSTRACT

According to some embodiments of the present disclosure, a method for configuring a drill bit comprises determining a number of blades of a drill bit. If the number of blades of the drill bit equals five, the method further comprises disposing each of a plurality of depth of cut controllers (DOCCs) on one of the blades of the drill bit such that each group of three radially consecutive DOCCs of the plurality of DOCCs is substantially force balanced. If the number of blades of the drill bit is greater than five, the method further comprises disposing each of the plurality of DOCCs on one of the blades of the drill bit such that each group of four radially consecutive DOCCs of the plurality of DOCCs is substantially force balanced.

TECHNICAL FIELD

The present disclosure relates generally to downhole drilling tools and, more particularly, to a system and method for improving the stability of drilling tools.

BACKGROUND

Various types of downhole drilling tools including, but not limited to, rotary drill bits, reamers, core bits, and other downhole tools have been used to form wellbores in associated downhole formations. Examples of such rotary drill bits include, but are not limited to, fixed cutter drill bits, drag bits, polycrystalline diamond compact (PDC) drill bits, and matrix drill bits associated with forming oil and gas wells extending through one or more downhole formations. Fixed cutter drill bits such as a PDC bit may include multiple blades that each include multiple cutting elements.

In typical drilling applications, a PDC bit may be used to drill through various levels or types of geological formations with longer bit life than non-PDC bits. Typical formations may generally have a relatively low compressive strength in the upper portions (e.g., shallower drilling depths) of the formation and a relatively high compressive strength in the lower portions (e.g., deeper drilling depths) of the formation.

A drilling tool may include one or more depth of cut controllers (DOCCs) configured to control the amount that a drilling tool cuts into the side of a geological formation. However, conventional DOCC configurations may be such that all the DOCCs configured to control the depth of cut of a drilling tool for a desired depth of cut may not be in contact with the formation at the same time. Accordingly, the DOCCs may not control the depth of cut of the cutting tools to the desired depth of cut and may unevenly control the depth of cut with respect to each other. Such uneven depth of cut control may result in imbalance forces and vibrations. Further, traditional layouts of DOCCs on a drilling tool may add to these imbalance forces.

SUMMARY

According to some embodiments of the present disclosure, a method for configuring a drill bit comprises determining a number of blades of a drill bit. If the number of blades of the drill bit equals five, the method further comprises disposing each of a plurality of depth of cut controllers (DOCCs) on one of the blades of the drill bit such that each group of three radially consecutive DOCCs of the plurality of DOCCs is substantially force balanced. If the number of blades of the drill bit is greater than five, the method further comprises disposing each of the plurality of DOCCs on one of the blades of the drill bit such that each group of four radially consecutive DOCCs of the plurality of DOCCs is substantially force balanced.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present disclosure and its features and advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates an example embodiment of a drilling system in accordance with some embodiments of the present disclosure;

FIG. 2 illustrates a bit face profile of a drill bit forming a wellbore, in accordance with some embodiments of the present disclosure;

FIG. 3 illustrates a blade profile that may represent a cross-sectional view of a blade of a drill bit, in accordance with some embodiments of the present disclosure;

FIG. 4A illustrates the face of a drill bit including a depth of cut controller (DOCC) having forces acting upon it during drilling, in accordance with some embodiments of the present disclosure;

FIG. 4B illustrates a bit face profile of the drill bit of FIG. 4A;

FIG. 5A illustrates the face of an example drill bit including DOCCs that may be substantially force balanced, in accordance with some embodiments of the present disclosure;

FIG. 5B illustrates a bit face profile of the drill bit of FIG. 5A;

FIG. 6A illustrates the face of another example drill bit including DOCCs that may be substantially force balanced, in accordance with some embodiments of the present disclosure;

FIG. 6B illustrates a bit face profile of the drill bit of FIG. 6A;

FIG. 7A illustrates the face of an example drill bit including five blades having DOCCs disposed thereon and force balanced in accordance with some embodiments of the present disclosure;

FIG. 7B illustrates a bit face profile of the drill bit of FIG. 7A;

FIG. 8A illustrates the face of an example drill bit including six blades having DOCCs disposed thereon and force balanced in accordance with some embodiments of the present disclosure;

FIG. 8B illustrates a bit face profile of the drill bit of FIG. 8A;

FIG. 9A illustrates the face of an example drill bit including seven blades having DOCCs disposed thereon and force balanced in accordance with some embodiments of the present disclosure;

FIG. 9B illustrates a bit face profile of the drill bit of FIG. 9A;

FIG. 10 illustrates the face of an example drill bit including eight blades having DOCCs disposed thereon and force balanced in accordance with some embodiments of the present disclosure;

FIG. 11 illustrates the face of an example drill bit including nine blades having DOCCs disposed thereon and force balanced in accordance with some embodiments of the present disclosure;

FIG. 12 illustrates an example method for disposing DOCCs on a drill bit such that the imbalance forces associated with the DOCCs acting on the drill bit may be reduced in accordance with some embodiments of the present disclosure;

FIG. 13 illustrates another example method for disposing DOCCs on a drill bit such that the imbalance forces associated with the DOCCs acting on the drill bit may be reduced in accordance with some embodiments of the present disclosure;

FIG. 14A illustrates the face of a drill bit for which a critical depth of cut control curve (CDCCC) may be determined, in accordance with some embodiments of the present disclosure;

FIG. 14B illustrates a bit face profile of the drill bit of FIG. 14A;

FIGS. 14C and 14D illustrate critical depth of cut control curves of the drill bit of FIG. 14A; and

FIG. 15 illustrates an example method of determining and generating a CDCCC in accordance with some embodiments of the present disclosure.

DETAILED DESCRIPTION

Embodiments of the present disclosure and its advantages are best understood by referring to FIGS. 1 through 15, where like numbers are used to indicate like and corresponding parts.

FIG. 1 illustrates an example embodiment of a drilling system 100 configured to drill into one or more geological formations, in accordance with some embodiments of the present disclosure. While drilling through geological formations, a variety of forces may act on components of a drilling tool such as the cutting elements and depth of cut controllers (DOCCs) of the drilling tool. Accordingly, a drilling tool may experience imbalance forces if the forces acting on each of the components of the drilling tool are not sufficiently balanced.

Imbalance forces may be created by a variety of factors associated with non-uniform downhole drilling conditions. For example, imbalance forces may be created when a drilling tool transitions from a first downhole formation to a second downhole formation that is harder than the first formation. Imbalance forces may also be created by drilling from a first downhole formation into a second downhole formation where the second downhole formation may be at an angle other than normal to the wellbore being formed by a downhole drilling tool. Further, imbalance forces may be created by different DOCCs coming in contact with the formation at different times. Such imbalance forces may result in vibrations to a drill string that may damage one or more components of the drill string. Accordingly, drilling system 100 may include downhole drilling tools (e.g., a drill bit, a reamer, a hole opener, etc.) configured to reduce imbalance forces applied to one or more components of drilling system 100 to improve the performance of drilling system 100.

As disclosed in further detail below and according to some embodiments of the present disclosure, a drilling tool may include DOCCs oriented on a drilling tool to improve the balance of forces acting on the drilling tool. Additionally, the DOCCs configured for a particular desired depth of cut may be configured such that they are in contact with the formation at substantially the same time to further improve the balance of forces acting on the drilling tool. Consequently, imbalance forces of a drilling tool associated with the DOCCs may be reduced or eliminated.

Drilling system 100 may include a well surface or well site 106. Various types of drilling equipment such as a rotary table, mud pumps and mud tanks (not expressly shown) may be located at a well surface or well site 106. For example, well site 106 may include a drilling rig 102 that may have various characteristics and features associated with a “land drilling rig.” However, downhole drilling tools incorporating teachings of the present disclosure may be satisfactorily used with drilling equipment located on offshore platforms, drill ships, semi-submersibles and drilling barges (not expressly shown).

Drilling system 100 may include a drill string 103 associated with drill bit 101 that may be used to form a wide variety of wellbores or bore holes such as generally vertical wellbore 114 a or generally horizontal wellbore 114 b as shown in FIG. 1. Various directional drilling techniques and associated components of a bottom hole assembly (BHA) 120 of drill string 103 may be used to form horizontal wellbore 114 b. For example, lateral forces may be applied to BHA 120 proximate kickoff location 113 to form horizontal wellbore 114 b extending from generally vertical wellbore 114 a.

BHA 120 may be formed from a wide variety of components configured to form a wellbore 114. For example, components 122 a, 122 b and 122 c of BHA 120 may include, but are not limited to, drill bits (e.g., drill bit 101), drill collars, rotary steering tools, directional drilling tools, downhole drilling motors, reamers, hole enlargers or stabilizers. The number of components such as drill collars and different types of components 122 included in BHA 120 may depend upon anticipated downhole drilling conditions and the type of wellbore that will be formed by drill string 103 and rotary drill bit 101.

A wellbore 114 may be defined in part by a casing string 110 that may extend from well surface 106 to a selected downhole location. Portions of a wellbore 114, as shown in FIG. 1, that do not include casing string 110 may be described as “open hole.” Various types of drilling fluid may be pumped from well surface 106 through drill string 103 to attached drill bit 101. Such drilling fluids may be directed to flow from drill string 103 to respective nozzles (not expressly shown) passing through rotary drill bit 101. The drilling fluid may be circulated back to well surface 106 through an annulus 108 defined in part by outside diameter 112 of drill string 103 and inside diameter 118 of wellbore 114 a. Inside diameter 118 may be referred to as the “sidewall” of wellbore 114 a. Annulus 108 may also be defined by outside diameter 112 of drill string 103 and inside diameter 111 of casing string 110.

Drilling system 100 may also include a rotary drill bit (“drill bit”) 101. Drill bit 101 may be any of various types of fixed cutter drill bits, including PDC bits, drag bits, matrix drill bits, and/or steel body drill bits operable to form wellbore 114 extending through one or more downhole formations. Drill bit 101 may be designed and formed in accordance with teachings of the present disclosure and may have many different designs, configurations, and/or dimensions according to the particular application of drill bit 101.

Drill bit 101 may include one or more blades 126 (e.g., blades 126 a-126 i) that may be disposed outwardly from exterior portions of bit body 124 of drill bit 101. Bit body 124 may have a generally cylindrical shape and blades 126 disposed on bit body 124 may be any suitable type of projections extending outwardly from rotary bit body 124. For example, a portion of blade 126 may be directly or indirectly coupled to an exterior portion of bit body 124, while another portion of blade 126 may be projected away from the exterior portion of bit body 124. Blades 126 formed in accordance with teachings of the present disclosure may have a wide variety of configurations including, but not limited to, substantially arched, helical, spiraling, tapered, converging, diverging, symmetrical, and/or asymmetrical.

In some cases, blades 126 may have substantially arched configurations, generally helical configurations, spiral shaped configurations, or any other configuration satisfactory for use with each downhole drilling tool. One or more blades 126 may have a substantially arched configuration extending from proximate rotational axis 104 of bit 101. The arched configuration may be defined in part by a generally concave, recessed shaped portion extending from proximate bit rotational axis (or rotational axis) 104. The arched configuration may also be defined in part by a generally convex, outwardly curved portion disposed between the concave, recessed portion and exterior portions of each blade which correspond generally with the outside diameter of the rotary drill bit.

In an embodiment of drill bit 101, blades 126 may include primary blades disposed generally symmetrically about rotational axis 104. For example, one embodiment may include three primary blades oriented approximately 120 degrees relative to each other with respect to rotational axis 104 in order to provide stability for drill bit 101. In some embodiments, blades 126 may also include at least one secondary blade disposed between the primary blades. The number and location of secondary blades and primary blades may vary substantially. Blades 126 may be disposed symmetrically or asymmetrically with regard to each other and rotational axis 104 where the disposition may be based on the downhole drilling conditions of the drilling environment.

Each of blades 126 may include a first end disposed proximate or toward rotational axis 104 and a second end disposed proximate or toward exterior portions of drill bit 101 (i.e., disposed generally away from rotational axis 104 and toward uphole portions of drill bit 101). The terms “downhole” and “uphole” may be used in this application to describe the location of various components of drilling system 100 relative to the bottom or end of a wellbore. For example, a first component described as “uphole” from a second component may be further away from the end of the wellbore than the second component. Similarly, a first component described as being “downhole” from a second component may be located closer to the end of the wellbore than the second component.

Each of blades 126 may have a leading (or front) surface disposed on one side of the blade in the direction of rotation of drill bit 101 and a trailing (or back) surface disposed on an opposite side of the blade away from the direction of rotation of drill bit 101. Blades 126 may be positioned along bit body 124 such that they have a spiral configuration relative to rotational axis 104. In other embodiments, blades 126 may be positioned along bit body 124 in a generally parallel configuration with respect to each other and rotational axis 104.

Blades 126 may have a general arcuate configuration extending radially from rotational axis 104. The arcuate configurations of blades 126 may cooperate with each other to define, in part, a generally cone shaped or recessed portion disposed adjacent to and extending radially outward from the rotational axis.

Blades 126 may include one or more cutting elements 128 disposed outwardly from exterior portions of each blade 126. For example, a portion of a cutting element 128 may be directly or indirectly coupled to an exterior portion of a blade 126 while another portion of the cutting element 128 may be projected away from the exterior portion of the blade 126. Cutting elements 128 may be any suitable device configured to cut into a formation, including but not limited to, primary cutting elements, backup cutting elements or any combination thereof. By way of example and not limitation, cutting elements 128 may be various types of cutters, compacts, buttons, inserts, and gage cutters satisfactory for use with a wide variety of drill bits 101.

In some embodiments of the present disclosure, cutting elements 128 may be disposed on blades 126 to improve the balance of forces acting on cutting elements 128. Therefore, imbalance forces associated with cutting elements 128 may be reduced in addition to reducing the imbalance forces associated with DOCCs.

Cutting elements 128 may include respective substrates with a layer of hard cutting material disposed on one end of each respective substrate. The hard layer of cutting elements 128 may provide a cutting surface that may engage adjacent portions of a downhole formation to form a wellbore 114. The contact of the cutting surface with the formation may form a cutting zone associated with each of cutting elements 128. The edge of the cutting surface located within the cutting zone may be referred to as the cutting edge of a cutting element 128.

Each substrate of cutting elements 128 may have various configurations and may be formed from tungsten carbide or other materials associated with forming cutting elements for rotary drill bits. Tungsten carbides may include, but are not limited to, monotungsten carbide (WC), ditungsten carbide (W₂C), macrocrystalline tungsten carbide and cemented or sintered tungsten carbide. Substrates may also be formed using other hard materials, which may include various metal alloys and cements such as metal borides, metal carbides, metal oxides and metal nitrides. For some applications, the hard cutting layer may be formed from substantially the same materials as the substrate. In other applications, the hard cutting layer may be formed from different materials than the substrate. Examples of materials used to form hard cutting layers may include polycrystalline diamond materials, including synthetic polycrystalline diamonds.

Blades 126 may also include one or more DOCCs (not expressly shown) configured to control the depth of cut of cutting elements 128. A DOCC may comprise an impact arrestor, a backup cutter and/or an MDR (Modified Diamond Reinforcement). Exterior portions of blades 126, cutting elements 128 and DOCCs may be described as forming portions of the bit face. As mentioned above and detailed below, the layout and disposition of the DOCCs on the face of drill bit 101 and blades 126 may be such that imbalance forces associated with the DOCCs may be reduced.

Blades 126 may further include one or more gage pads (not expressly shown) disposed on blades 126. A gage pad may be a gage, gage segment, or gage portion disposed on exterior portion of a blade 126. Gage pads may often contact adjacent portions of a wellbore 114 formed by drill bit 101. Exterior portions of blades 126 and/or associated gage pads may be disposed at various angles, either positive, negative, and/or parallel, relative to adjacent portions of a straight wellbore (e.g., wellbore 114 a). A gage pad may include one or more layers of hardfacing material.

The rate of penetration (ROP) of drill bit 101 is often a function of both weight on bit (WOB) and revolutions per minute (RPM). Drill string 103 may apply weight on drill bit 101 and may also rotate drill bit 101 about rotational axis 104 to form a wellbore 114 (e.g., wellbore 114 a or wellbore 114 b). For some applications a downhole motor (not expressly shown) may be provided as part of BHA 120 to also rotate drill bit 101. The depth of cut controlled by DOCCs (not expressly shown) and blades 126 may also be based on the ROP and RPM of a particular bit. Accordingly, as described in further detail below, the configuration of the DOCCs to provide an improved depth of cut of cutting elements 128 may be based in part on the desired ROP and RPM of a particular drill bit 101.

FIG. 2 illustrates bit face profile 200 that may represent a cross-sectional view of drill bit 101. In the present embodiment, drill bit 101 may be configured to form a wellbore through a first formation layer 202 into a second formation layer 204, in accordance with some embodiments of the present disclosure. Exterior portions of blades (not expressly shown), cutting elements 128 and DOCCs (not expressly shown) may be projected rotationally onto a radial plane to form bit face profile 200. In the illustrated embodiment, formation layer 202 may be described as “softer” or “less hard” when compared to downhole formation layer 204. As mentioned above and discussed in further detail below, the placement of DOCCs on blades 126 of drill bit 101 may be such that imbalance forces that may result from a transition from formation layer 202 to formation layer 204 may be reduced.

As shown in FIG. 2, exterior portions of drill bit 101 that contact adjacent portions of a downhole formation may be described as a “bit face.” Bit face profile 200 of drill bit 101 may include various zones or segments. Bit face profile 200 may be substantially symmetric about rotational axis 104 due to the rotational projection of bit face profile 200, such that the zones or segments on one side of rotational axis 104 may be substantially similar to the zones or segments on the opposite side of rotational axis 104.

For example, bit face profile 200 may include gage zone 206 a located opposite gage zone 206 b, shoulder zone 208 a located opposite shoulder zone 208 b, nose zone 210 a located opposite nose zone 210 b, and cone zone 212 a located opposite cone zone 212 b. Cutting elements 128 included in each zone may be referred to as cutting elements of that zone. For example, cutting elements 128 _(g) included in gage zones 206 may be referred to as gage cutting elements, cutting elements 128 _(s) included in shoulder zones 208 may be referred to as shoulder cutting elements, cutting elements 128 _(n) included in nose zones 210 may be referred to as nose cutting elements, and cutting elements 128 _(c) included in cone zones 212 may be referred to as cone cutting elements. As discussed in further detail below with respect to FIG. 3, each zone or segment along bit face profile 200 may be defined in part by respective portions of associated blades 126.

Cone zones 212 may be generally convex and may be formed on exterior portions of each blade (e.g., blades 126 as illustrated in FIG. 1) of drill bit 101, adjacent to and extending out from rotational axis 104. Nose zones 210 may be generally convex and may be formed on exterior portions of each blade of drill bit 101, adjacent to and extending from each cone zone 212. Shoulder zones 208 may be formed on exterior portions of each blade 126 extending from respective nose zones 210 and may terminate proximate to a respective gage zone 206.

FIG. 3 illustrates bit face profile 300 that represents another cross-sectional view of drill bit 101. Bit face profile 300 may represent drill bit 101. A comparison of FIGS. 2 and 3 shows that bit face profile 300 of FIG. 3 is inverted with respect to bit face profile 200 of FIG. 2.

A coordinate on the graph in FIG. 3 corresponding to rotational axis 104 may be referred to as an axial coordinate or position. A coordinate on the graph in FIG. 3 corresponding to reference line 301 may be referred to as a radial coordinate or radial position that may indicate a distance extending orthogonally from rotational axis 104 in a radial plane passing through rotational axis 104. For example, in FIG. 3 rotational axis 104 may be placed along a z-axis and reference line 301 may indicate the distance (R) extending orthogonally from rotational axis 104 to a point on a radial plane that may be defined as the ZR plane.

According to the present disclosure and as detailed below, DOCCs (not expressly shown) disposed along bit face profiles 200 and 300 may be disposed on blades 126 and oriented on the face of drill bit 101 to reduce the imbalance of forces acting on drill bit 101. As discussed further with respect to FIGS. 4-11, the placement of each DOCC on the face of drill bit 101 to reduce the imbalance forces may be such that groups of DOCCs consecutively placed in the radial plane may be substantially force balanced. Such force balancing may be based on the number of blades 126, the number of DOCCs and the number of DOCCs in each group of radially consecutive DOCCs. Additionally, the axial position of the each DOCC may be adjusted such that each DOCC configured for a desired depth of cut of drill bit 101 may be in contact with the formation at substantially the same time to reduce imbalance forces associated with the DOCCs.

FIGS. 2 and 3 are for illustrative purposes only and modifications, additions or omissions may be made to FIGS. 2 and 3 without departing from the scope of the present disclosure. For example, the actual locations of the various zones with respect to the bit face profile may vary and may not be exactly as depicted.

FIG. 4A illustrates the face of drill bit 401 including DOCC 402 having forces acting upon it during drilling, in accordance with some embodiments of the present disclosure. FIG. 4B illustrates a bit face profile of drill bit 401 of FIG. 4A. To provide a frame of reference, FIG. 4B may include a coordinate system similar to that of FIG. 3 and includes a z-axis that may represent rotational axis 404 of drill bit 401. Accordingly, a coordinate or position corresponding to the z-axis of FIG. 4B may be referred to as an axial coordinate or axial position of the bit face profile depicted in FIG. 4B. FIG. 4B also includes a radial axis (R) that indicates the orthogonal distance from rotational axis 404 of drill bit 401.

Additionally, a location along the bit face of drill bit 401 as shown in FIG. 4A may be described by x and y coordinates of an xy-plane of FIG. 4A. The xy-plane of FIG. 4A may be substantially perpendicular to the z-axis of FIG. 4B such that the xy-plane of FIG. 4A may be substantially perpendicular to rotational axis 404 of drill bit 401. Additionally, the x-axis and y-axis of FIG. 4A may intersect each other at the z-axis of FIG. 4B such that the x-axis and y-axis may intersect each other at rotational axis 404 of drill bit 401.

The distance from rotational axis 404 of the drill bit 401 to a point in the xy plane of the bit face of FIG. 4A may indicate the radial coordinate or radial position of the point on the bit face profile depicted in FIG. 4B. For example, the radial coordinate, r, of a point in the xy plane having an x coordinate, x, and a y coordinate, y, may be expressed by the following equation:

r=√{square root over (x ² +y ²)}

Additionally, a point in the xy plane (of FIG. 4A) may have an angular coordinate that may be an angle between a line extending orthogonally from rotational axis 404 of drill bit 401 to the point and the x-axis. For example, the angular coordinate (θ) of a point in the xy plane (of FIG. 4B) having an x-coordinate, x, and a y-coordinate, y, may be expressed by the following equation:

θ=arctan(y/x)

The cited coordinates and coordinate systems are used for illustrative purposes only, and any other suitable coordinate system or configuration, may be used to provide a frame of reference of points along the bit face profile and bit face of a drill bit associated with FIGS. 4A and 4B, without departing from the scope of the present disclosure. Additionally, any suitable units may be used. For example, the angular position may be expressed in degrees or in radians.

Returning to FIG. 4A, drill bit 401 may include DOCC 402 disposed on blades 426. In the present illustration, one DOCC 402 is depicted but drill bit 401 may include additional DOCCs disposed on any one of blades 426. Additionally, blades 426 may also include cutting elements (not expressly shown) and DOCC 402 may control the depth of cut of one or more of these cutting elements.

As mentioned above, a variety of forces may act on DOCC 402 when DOCC 402 is in contact with a formation while drilling. These forces may include frictional force (F_(f)) 405 (also referred to as drag force), radial force (F_(r)) 407, both of which are depicted in FIG. 4A, and normal force (F_(n)) 411, which is depicted in FIG. 4B.

The combination of frictional force 405 and radial force 407 may result in lateral force 409 acting upon drill bit 401 such that frictional force 405 and radial force 407 may be vector components of lateral force 409 of drill bit 401. The sum of frictional forces 405 and radial forces 407 acting on each DOCC 402 may represent the overall lateral force 409 acting on drill bit 401 due to DOCCs 402. Lateral force 409 may, if unbalanced, cause a lateral moment to be exerted on drill bit 401, which may cause drill bit 401 to vibrate, veer in an undesirable direction or any combination thereof. Accordingly, as detailed below, DOCCs 402 may be disposed on blades 426 to improve the balance of their respective frictional forces 405 and radial forces 407 such that lateral force 409 and its associated lateral moment may be reduced.

Normal force 411 associated with DOCC 402 may include the forces acting on DOCC 402 that are perpendicular to the surface of DOCC 402, as shown in FIG. 4B. Normal force 411 may include a vector component radial force (F_(r)) 415 (which may be part of the sum of forces that equals radial force 407 of FIG. 4A) and vector component axial force (F_(a)) 413. Axial force 413 may represent the forces acting on DOCC 402 that are parallel to rotational axis 404 of drill bit 401. Axial force 413 may generate an axial moment acting on drill bit 401 that may be represented by multiplying axial force 413 by the radial distance of DOCC 402 from rotational axis 404. For example, in the present illustration, DOCC 402 may have a radial distance of “L” from rotational axis 404 such that the axial moment (M_(a)) associated with DOCC 402 acting on drill bit 401 may be expressed by the following equation:

M _(a) =F _(a) *L.

DOCCs 402 may be disposed on blades 426 such that the axial moments of DOCCs 402 may be substantially balanced to reduce an overall axial moment of drill bit 401. Such reduction in the axial moment may reduce vibrations and maintain the desired trajectory of drill bit 401.

Modifications, additions, or omissions may be made to FIGS. 4A and 4B without departing from the scope of the present disclosure. For example, as mentioned previously, drill bit 401 may include any number of DOCCs 402, disposed on any number of blades 426 in a manner that improves the balance of forces acting on drill bit 401. As discussed in further detail below, DOCCs 402 may be organized into groups of radially consecutive DOCCs 402 that may be in contact with a formation being drilled to balance the forces acting on drill bit 401. Additionally, although not expressly shown, drill bit 401 may include one or more cutting elements.

FIG. 5A illustrates the face of drill bit 501 including DOCCs 502 a, 502 b, and 502 c that may be a group of three radially consecutive DOCCs that are substantially force balanced, in accordance with some embodiments of the present disclosure. FIG. 5B illustrates a bit face profile of drill bit 501 of FIG. 5A. The orientation of DOCCs 502 a-502 c on drill bit 501 of FIGS. 5A and 5B may include a coordinate system similar to that of FIGS. 4A and 4B. Drill bit 501 may also include one or more cutting elements not expressly shown.

Drill bit 501 may include blades 526 a-526 e. Blade 526 a may include DOCC 502 a disposed thereon, blade 526 b may include DOCC 502 b disposed thereon, and blade 526 d may include DOCC 502 c disposed thereon. DOCC 502 a may have a radial location closest to rotational axis 504 of drill bit 501. The radial location of DOCC 502 b may overlap the radial location of DOCC 502 a by less than 100% and may be further from rotational axis 504 in the radial plane than DOCC 502 a. In the present embodiment, DOCC 502 b may be an adjacent or “neighbor” DOCC to DOCC 502 a in the radial direction because DOCCs 502 a and 502 b may be next to each other in the radial plane. The radial location of DOCC 502 b may overlap the radial location of DOCC 502 a by less than 100% and may be further from rotational axis 504 and cone zone 512 in the radial plane than DOCC 502 b. DOCC 502 c may be an adjacent or “neighbor” DOCC to DOCC 502 b because DOCCs 502 b and 502 c may be next to each other in the radial plane. With DOCCs 502 a-502 c being placed outward radially from rotational axis 504 toward the edge of drill bit 501, DOCCs 502 a, 502 b, and 502 c may be referred to as radially consecutive DOCCs going from DOCC 502 a to DOCC 502 c.

In the illustrated embodiment of FIG. 5A, DOCCs 502 a, 502 b, and 502 c may be disposed on blades 526 a, 526 b, and 526 d, respectively, such that DOCCs 502 a, 502 b and 502 c are spaced approximately 120 degrees from each other with respect to rotational axis 504. In such a configuration where DOCCs 502 a-502 c are spaced in a generally symmetrical manner on the face of drill bit 501 the imbalance forces associated with DOCCs 502 a, 502 b, and 502 c may at least partially counteract each other.

For example, DOCCs 502 a, 502 b, and 502 c may have associated radial forces 507 a, 507 b, and 507 c, respectively and associated frictional forces 505 a, 505 b, and 505 c, respectively. Frictional forces 505 a, 505 b, and 505 c and radial forces 507 a, 507 b, and 507 c may result in lateral forces 509 a, 509 b, and 509 c acting on drill bit 501, similarly to lateral forces 409 acting on drill bit 401 described above with respect to FIG. 4A. As shown in FIG. 5A, the directions of lateral forces 509 a, 509 b, and 509 c may at least partially oppose each other such that lateral forces 509 a, 509 b, and 509 c may at least partially cancel each other out. Accordingly, the overall lateral force and its associated lateral moment associated with DOCCs 502 a-502 c acting on drill bit 501 may be reduced and/or minimized. Such a configuration may be desirable because as the overall lateral forces and lateral moments approach zero, vibrations of drill bit 501 and its associated BHA and drill string may also be reduced, which may reduce wear on the components and improve drilling performance.

Further, as shown in FIG. 5B, axial forces 513 a, 513 b, and 513 c may be associated with DOCCs 502 a, 502 b, and 502 c, respectively. With DOCCs 502 a, 502 b, and 502 c disposed on drill bit 501 in a generally symmetrical manner as depicted in FIG. 5A, axial forces 513 a, 513 b, and 513 c may be acting on different areas of the face of drill bit 501 such that the axial moments associated with axial forces 513 a, 513 b, and 513 c may at least partially counteract each other.

Therefore, the overall imbalance forces and moments (e.g., lateral and axial forces and moments) associated with DOCCs 502 a-502 c acting on drill bit 501 may be reduced and/or minimized. DOCCs 502 a, 502 b, and 502 c configured as shown and described in FIGS. 5A and 5B may be referred to as a force balanced group of three radially consecutive DOCCs.

Additionally, as detailed below with respect to FIGS. 12, 14A-14D, and 15, the axial positions of DOCCs 502 a, 502 b, and 502 c may be configured such that each of DOCCs 502 a, 502 b, and 502 c are in contact with a formation at approximately the same time for a desired depth of cut. Accordingly, imbalance forces associated with DOCCS 502 a-502 c not being in contact with the formation at approximately the same time may be reduced.

Modifications, additions, or omissions may be made to drill bit 501 without departing from the scope of the present disclosure. For example, a group of DOCCs 502 may be located within and/or overlap with a different zone (e.g., cone zone 512, shoulder zone 508, gage zone 506 a, etc.) of drill bit 501. Additionally, a drill bit may include more or fewer blades and/or DOCCs that may be force balanced according to the particular number of blades and DOCCs that may be in contact with a formation at a time.

For example, FIG. 6A illustrates the face of drill bit 601 including DOCCs 602 a, 602 b, 602 c, and 602 d that may be a group of four radially consecutive DOCCs that are substantially force balanced, in accordance with some embodiments of the present disclosure. FIG. 6B illustrates a bit face profile of drill bit 601 of FIG. 6A. The orientation of DOCCs 602 a-602 d on drill bit 601 of FIGS. 6A and 6B may be referred to using a coordinate system similar to that of FIGS. 4A and 4B. Drill bit 601 may also include one or more cutting elements not expressly shown.

Drill bit 601 may include blades 626 a-626 d with DOCCs 602 a-602 d respectively disposed thereon. In the illustrated embodiment, DOCCs 602 a-602 d may be placed outward radially with DOCC 602 a disposed closest to rotational axis 604 in the radial direction and DOCC 602 d disposed closest to the edge of drill bit 601. Accordingly, similar to DOCCs 502 a-502 c of FIGS. 5A and 5B, DOCCs 602 a-602 d may be referred to as radially consecutive DOCCs going from DOCC 602 a to DOCC 602 d.

In the illustrated embodiment in FIG. 6A, DOCCs 602 a-602 d may be disposed on blades 626 a-626 d, respectively, such that DOCCs 602 a-602 d are spaced approximately 90 degrees from each other with respect to rotational axis 604. Similar to described above with respect to DOCCs 502 a-502 c of FIGS. 5A and 5B, in such a configuration where DOCCs 602 a-602 d are spaced in a generally symmetrical manner on the face of drill bit 601 the imbalance forces and moments associated with DOCCs 602 a-602 d may at least partially counteract each other.

For example, DOCCs 602 a, 602 b, 602 c, and 602 d may have associated radial forces 607 a, 607 b, 607 c, and 607 c, respectively and associated frictional forces 605 a, 605 b, 605 c, and 605 d, respectively. Frictional forces 605 a, 605 b, 605 c, and 605 d and radial forces 607 a, 607 b, 607 c, and 607 c, may result in lateral forces 609 a, 609 b, 609 c, and 609 d acting on drill bit 601, similarly to lateral forces 409 acting on drill bit 401 described above with respect to FIG. 4A and lateral forces 509 a-509 c acting on drill bit 501 described above with respect to FIG. 5A. As shown in FIG. 6A, the directions of lateral forces 609 a, 609 b, 609 c, and 609 d may at least partially oppose each other such that lateral forces 609 a, 609 b, 609 c, and 609 d may at least partially cancel each other out. Accordingly, the overall lateral force and its associated lateral moment associated with DOCCs 602 a-602 d acting on drill bit 601 may be reduced and/or minimized.

Further, as shown in FIG. 6B, axial forces 613 a, 613 b, 613 c, and 613 d may be associated with DOCCs 602 a, 602 b, 602 c, and 602 d, respectively. With DOCCs 602 a, 602 b, 602 c, and 602 d disposed on drill bit 601 in a generally symmetrical manner as depicted in FIG. 6A, axial forces 613 a, 613 b, 613 c, and 613 d may be acting on different areas of the face of drill bit 601 such that the axial moments associated with axial forces 613 a, 613 b, 613 c, and 613 d may at least partially counteract each other.

Therefore, the overall imbalance forces and moments (e.g., lateral and axial forces and moments) associated with DOCCs 602 a-602 d acting on drill bit 601 may be reduced and/or minimized. DOCCs 602 a, 602 b, 602 c, and 602 d configured as shown and described in FIGS. 6A and 6B may be referred to as a force balanced group of four radially consecutive DOCCs.

Additionally, as described below with respect to FIGS. 13, 14A-14D, and 15, the axial positions of DOCCs 602 a-602 d may be configured such that each of DOCCs 602 a, 602 b, 602 c, and 602 d are in contact with a formation at approximately the same time at a desired depth of cut. Accordingly, imbalance forces associated with DOCCS 602 a-602 d not being in contact with the formation at approximately the same time may be reduced.

Modifications, additions, or omissions may be made to drill bit 601 without departing from the scope of the present disclosure. For example, a group of DOCCs 602 may be located within and/or overlap with a different zone (e.g., cone zone 612, shoulder zone 608, gage zone 606 a, etc.) of drill bit 601. Additionally, a drill bit may include more or fewer blades and/or DOCCs that may be force balanced according to the particular number of blades and DOCCs that may be in contact with a formation at a time. Further, FIGS. 6A and 6B are used to show a layout of four radially consecutive DOCCs that are substantially force balanced on drill bit 601 with four blades. However, as described in further detail below with respect to FIGS. 8A-11, and 13, drill bits having more than five blades may also have one or more force balanced groups of four radially consecutive DOCCs.

As described above, DOCCs of drill bits may be configured in force balanced groups of three radially consecutive DOCCs and force balanced groups of four radially consecutive DOCCs (among other force balanced groups of N number of radially consecutive DOCCs). As described in detail below with respect to FIGS. 7A, 7B, and 12, imbalance forces associated with DOCCs of a drill bit having five blades may be reduced and/or minimized by disposing the DOCCs on the five bladed drill bit such that every group of three radially consecutive DOCCs of the drill bit is substantially force balanced. Additionally, as described below with respect to FIGS. 8A-11 and 13, imbalance forces associated with DOCCs of a drill bit having more than five blades may be reduced and/or minimized by disposing the DOCCs such that every group of four radially consecutive DOCCs is substantially force balanced. Additionally, the axial positions of the DOCCs may be determined according to the present disclosure such that each DOCC associated with a desired depth of cut is in contact with a formation at approximately the same time. Therefore, drill bits designed in accordance with the teachings of the present disclosure may have improved force balancing and a reduction in vibrations, which may reduce strain and wear on one or more components of an associated drill string.

FIG. 7A illustrates the face of drill bit 701 including five blades (blades 726 a-726 e) having DOCCs (DOCCs 702 a-702 j) disposed thereon and force balanced in accordance with some embodiments of the present disclosure. FIG. 7B illustrates a bit face profile of drill bit 701 of FIG. 7A. Drill bit 701 may also include one or more cutting elements not expressly shown.

In the illustrated embodiment as shown in FIGS. 7A and 7B, DOCCs 702 a-702 j may be increasingly disposed outward from a rotational axis 704 of drill bit 701 such that DOCCs 702 a-702 j may be considered radially consecutive DOCCs going from DOCC 702 a to DOCC 702 j. As described in detail below, DOCCs 702 a-702 j may be disposed on blades 726 a-726 e such that any group of three radially consecutive DOCCs 702 may be forced balanced. Such a configuration may allow for increased balance and stability of drill bit 701.

For example, DOCCs 702 a-702 j may be organized into the following groups of three radially consecutive DOCCs: (702 a, 702 b, 702 c); (702 b, 702 c, 702 d); (702 c, 702 d, 702 e); (702 d, 702 e, 702 f); (702 e, 702 f, 702 g); (702 f, 702 g, 702 h); (702 g, 702 h, 702 i); and (702 h, 702 i, 702 j). As shown in FIG. 7A, each DOCC 702 in the groups of three radially consecutive DOCCs is spaced from the other DOCCs in its respective group in a generally symmetrical manner (e.g., spaced from each other between approximately 100 degrees and 140 degrees with respect to rotational axis 704) such that the imbalance forces associated with each DOCC 702 of a particular group of three radially consecutive DOCCs 702 may at least partially counteract each other. For example, DOCCs 702 a, 702 b, and 702 c are spaced such that the imbalance forces associated with each of DOCCs 702 a, 702 b and 702 c may at least partially counteract each other. Accordingly, the overall imbalance forces associated with DOCCs 702 a-702 j as experienced by drill bit 701 may be reduced or minimized. The placement of DOCCs 702 a-702 j on the face of drill bit 701 such that each radially consecutive group of three DOCCs may be force balanced according to method 1200 described with respect to FIG. 12 below.

Additionally, the axial positions of DOCCs 702 a-702 j may be configured such that each of DOCCs 702 a-702 j is in contact with the formation being drilled at approximately the same time. Such adjustments may be made by calculating a critical depth of cut control curve (CDCCC) with respect to drill bit 701. Calculation of the CDCCC is described in detail with respect to FIGS. 14 and 15 below.

Modifications, additions, or omissions may be made to FIGS. 7A and 7B without departing from the scope of the present disclosure. For example, various configurations of DOCCs 702 a-702 j disposed on blades 726 a-726 e may result in each group of three radially consecutive DOCCs being force balanced. The illustrated disposition of DOCCs 702 a-702 j on drill bit 701 is merely one example of DOCCs 702 a-702 j disposed in force balance groups of three radially consecutive DOCCs on a drill bit including five blades.

FIG. 8A illustrates the face of a drill bit 801 including six blades (blades 826 a-826 f) having twelve DOCCs (DOCCs 802 a-802 l) disposed thereon and force balanced in accordance with some embodiments of the present disclosure. FIG. 8B illustrates a bit face profile of drill bit 801 of FIG. 8A. Drill bit 801 may also include one or more cutting elements not expressly shown.

In the present embodiment as shown in FIGS. 8A and 8B, DOCCs 802 a-802 l may be increasingly disposed outward from a rotational axis 804 of drill bit 801 such that DOCCs 802 a-802 l may be considered radially consecutive DOCCs going from DOCC 802 a to DOCC 802 l. As described in detail below, DOCCs 802 a-802 l may be disposed on blades 826 a-826 f such that any group of four radially consecutive DOCCs 802 may be forced balanced. Such a configuration may allow for increased balance and stability of drill bit 801.

For example, DOCCs 802 a-802 l may be organized into the following groups of four radially consecutive DOCCs 802: (802 a, 802 b, 802 c, 802 d); (802 b, 802 c, 802 d, 802 e); (802 c, 802 d, 802 e, 802 f); (802 d, 802 e, 802 f, 802 g); (802 e, 802 f, 802 g, 802 h); (802 f, 802 g, 802 h, 802 i); (802 g, 802 h, 802 i, 802 j); (802 h, 802 i, 802 j, 802 k); and (802 i, 802 j, 802 k, 802 l). As shown in FIG. 8A, each DOCC 802 in the groups of four radially consecutive DOCCs is spaced from the other DOCCs 802 in its respective group in a generally symmetrical manner (e.g., spaced from each other between approximately 75 degrees and 105 degrees with respect to rotational axis 804) such that the imbalance forces associated with each DOCC 802 of a particular group of four DOCCs 802 may at least partially counteract each other. For example, DOCCs 802 a, 802 b, 802 c, and 802 d are spaced such that the imbalance forces associated with each of DOCCs 802 a, 802 b, 802 c, and 802 d may at least partially counteract each other. Accordingly, the overall imbalance forces associated with DOCCs 802 a-802 l as experienced by drill bit 801 may be reduced or minimized. The placement of DOCCs 802 a-802 l on the face of drill bit 801 such that each radially consecutive group of four DOCCs may be force balanced may be done according to method 1300 described with respect to FIG. 13 below.

Additionally, the axial positions of DOCCs 802 a-802 l may be configured such that each of DOCCs 802 a-802 l is in contact with the formation being drilled at approximately the same time. Such adjustments may be made by calculating a critical depth of cut control curve (CDCCC) with respect to drill bit 801. Calculation of the CDCCC is described in detail with respect to FIGS. 14 and 15 below.

Modifications, additions, or omissions may be made to FIGS. 8A and 8B without departing from the scope of the present disclosure. For example, various configurations of DOCCs 802 a-802 l disposed on blades 826 a-826 f may result in each group of four radially consecutive DOCCs being force balanced. The illustrated disposition of DOCCs 802 a-802 l on drill bit 801 is merely one example of DOCCs 802 a-802 l disposed in force balance groups of four radially consecutive DOCCs on a drill bit including six blades.

FIG. 9A illustrates the face of a drill bit 901 including seven blades (blades 926 a-926 g) having fourteen DOCCs (DOCCs 902 a-902 n) disposed thereon and force balanced in accordance with some embodiments of the present disclosure. FIG. 9B illustrates a bit face profile of drill bit 901 of FIG. 9A. Drill bit 901 may also include one or more cutting elements not expressly shown.

In the present embodiment as shown in FIGS. 9A and 9B, DOCCs 902 a-902 n may be increasingly disposed outward from a rotational axis 904 of drill bit 901 such that DOCCs 902 a-902 n may be considered radially consecutive DOCCs going from DOCC 902 a to DOCC 902 n. As described in detail below, DOCCs 902 a-902 n may be disposed on blades 926 a-926 g such that any group of four radially consecutive DOCCs 902 may be forced balanced. Such a configuration may allow for increased balance and stability of drill bit 901.

For example, as shown in FIG. 9A, each DOCC 902 in the groups of four radially consecutive DOCCs is spaced from the other DOCCs 902 in its respective group in a generally symmetrical manner (e.g., spaced from each other between approximately 75 degrees and 105 degrees with respect to rotational axis 904) such that the imbalance forces associated with each DOCC 902 of a particular group of four DOCCs 902 may at least partially counteract each other. For example, DOCCs 902 a, 902 b, 902 c, and 902 d are spaced such that the imbalance forces associated with each of DOCCs 902 a, 902 b, 902 c, and 902 d may at least partially counteract each other. Accordingly, the overall imbalance forces associated with DOCCs 902 a-902 n as experienced by drill bit 901 may be reduced or minimized. The placement of DOCCs 902 a-902 n on the face of drill bit 901 such that each radially consecutive group of four DOCCs may be force balanced may be done according to method 1300 described with respect to FIG. 13 below.

Additionally, the axial positions of DOCCs 902 a-902 n may be configured such that each of DOCCs 902 a-902 n is in contact with the formation being drilled at approximately the same time. Such adjustments may be made by calculating a critical depth of cut control curve (CDCCC) with respect to drill bit 901. Calculation of the CDCCC is described in detail with respect to FIGS. 14 and 15 below.

Modifications, additions, or omissions may be made to FIGS. 9A and 9B without departing from the scope of the present disclosure. For example, various configurations of DOCCs 902 a-902 n disposed on blades 926 a-926 g may result in each group of four radially consecutive DOCCs being force balanced. The illustrated disposition of DOCCs 902 a-902 n on drill bit 901 is merely one example of DOCCs 902 a-902 n disposed in force balance groups of four radially consecutive DOCCs on a drill bit including seven blades.

FIG. 10 illustrates the face of a drill bit 1001 including eight blades (blades 1026 a-1026 h) having sixteen DOCCs (DOCCs 1002 a-1002 p) disposed thereon and force balanced in accordance with some embodiments of the present disclosure. Drill bit 1001 may also include one or more cutting elements not expressly shown.

In the present embodiment as shown in FIG. 10, DOCCs 1002 a-1002 p may be increasingly disposed outward from a rotational axis 1004 of drill bit 1001 such that DOCCs 1002 a-1002 p may be considered radially consecutive DOCCs going from DOCC 1002 a to DOCC 1002 p. As described in detail below, DOCCs 1002 a-1002 p may be disposed on blades 1026 a-1026 h such that any group of four radially consecutive DOCCs 1002 may be forced balanced. Such a configuration may allow for increased balance and stability of drill bit 1001.

For example, as shown in FIG. 10, each DOCC 1002 in the groups of four radially consecutive DOCCs is spaced from the other DOCCs 1002 in its respective group in a generally symmetrical manner (e.g., spaced from each other between approximately 75 degrees and 105 degrees with respect to rotational axis 1004) such that the imbalance forces associated with each DOCC 1002 of a particular group of four DOCCs 1002 may at least partially counteract each other. For example, DOCCs 1002 a, 1002 b, 1002 c, and 1002 d are spaced such that the imbalance forces associated with each of DOCCs 1002 a, 1002 b, 1002 c, and 1002 d may at least partially counteract each other. Accordingly, the overall imbalance forces associated with DOCCs 1002 a-1002 p as experienced by drill bit 1001 may be reduced or minimized. The placement of DOCCs 1002 a-1002 p on the face of drill bit 1001 such that each radially consecutive group of four DOCCs may be force balanced may be done according to method 1300 described with respect to FIG. 13 below.

Additionally, the axial positions of DOCCs 1002 a-1002 p may be configured such that each of DOCCs 1002 a-1002 p is in contact with the formation being drilled at approximately the same time. Such adjustments may be made by calculating a critical depth of cut control curve (CDCCC) with respect to drill bit 1001. Calculation of the CDCCC is described in detail with respect to FIGS. 14 and 15 below.

Modifications, additions, or omissions may be made to FIG. 10 without departing from the scope of the present disclosure. For example, various configurations of DOCCs 1002 a-1002 p disposed on blades 1026 a-1026 h may result in each group of four radially consecutive DOCCs being force balanced. The illustrated disposition of DOCCs 1002 a-1002 p on drill bit 1001 is merely one example of DOCCs 1002 a-1002 p disposed in force balance groups of four radially consecutive DOCCs on a drill bit including eight blades.

FIG. 11 illustrates the face of a drill bit 1101 including nine blades (blades 1126 a-1126 i) having eighteen DOCCs (DOCCs 1102 a-1102 r) disposed thereon and force balanced in accordance with some embodiments of the present disclosure. Drill bit 1101 may also include one or more cutting elements not expressly shown.

In the present embodiment as shown in FIG. 11, DOCCs 1102 a-1102 r may be increasingly disposed outward from a rotational axis 1104 of drill bit 1101 such that DOCCs 1102 a-1102 r may be considered radially consecutive DOCCs going from DOCC 1102 a to DOCC 1102 r. As described in detail below, DOCCs 1102 a-1102 r may be disposed on blades 1126 a-1126 i such that any group of four radially consecutive DOCCs 1102 may be forced balanced. Such a configuration may allow for increased balance and stability of drill bit 1101.

For example, as shown in FIG. 11, each DOCC 1102 in the groups of four radially consecutive DOCCs is spaced from the other DOCCs 1102 in its respective group in a generally symmetrical manner (e.g., spaced from each other between approximately 75 degrees and 105 degrees with respect to rotational axis 1104) such that the imbalance forces associated with each DOCC 1102 of a particular group of four DOCCs 1102 may at least partially counteract each other. For example, DOCCs 1102 a, 1102 b, 1102 c, and 1102 d are spaced such that the imbalance forces associated with each of DOCCs 1102 a, 1102 b, 1102 c, and 1102 d may at least partially counteract each other. Accordingly, the overall imbalance forces associated with DOCCs 1102 a-1102 r as experienced by drill bit 1101 may be reduced or minimized. The placement of DOCCs 1102 a-1102 r on the face of drill bit 1101 such that each radially consecutive group of four DOCCs may be force balanced may be done according to method 1300 described with respect to FIG. 13 below.

Additionally, the axial positions of DOCCs 1102 a-1102 r may be configured such that each of DOCCs 1102 a-1102 r are in contact with the formation being drilled at approximately the same time. Such adjustments may be made by calculating a critical depth of cut control curve (CDCCC) with respect to drill bit 1101. Calculation of the CDCCC is described in detail with respect to FIGS. 14 and 15 below.

Modifications, additions, or omissions may be made to FIG. 11 without departing from the scope of the present disclosure. For example, various configurations of DOCCs 1102 a-1102 r disposed on blades 1126 a-1126 i may result in each group of four radially consecutive DOCCs being force balanced. The illustrated disposition of DOCCs 1102 a-1102 r on drill bit 1101 is merely one example of DOCCs 1102 a-1102 r disposed in force balance groups of four radially consecutive DOCCs on a drill bit including nine blades.

FIG. 12 illustrates an example method 1200 for disposing DOCCs on a drill bit such that the imbalance forces associated with the DOCCs acting on the drill bit may be reduced. Method 1200 may be used to dispose DOCCs on a drill bit such that each group of three radially consecutive DOCCs may be substantially force balanced. For illustrative purposes, method 1200 is described with respect to drill bit 701 of FIGS. 7A and 7B; however, method 1200 may be performed with respect to any suitable drill bit.

The steps of method 1200 may be performed by various computer programs, models or any combination thereof, configured to simulate and design drilling systems, apparatuses and devices. The programs and models may include instructions stored on a computer readable medium and operable to perform, when executed, one or more of the steps described below. The computer readable media may include any system, apparatus or device configured to store and retrieve programs or instructions such as a hard disk drive, a compact disc, flash memory or any other suitable device. The programs and models may be configured to direct a processor or other suitable unit to retrieve and execute the instructions from the computer readable media. Collectively, the computer programs and models used to simulate and design drilling systems may be referred to as a “drilling engineering tool” or “engineering tool.”

Method 1200 may start, and at step 1202, the engineering tool may determine the desired radial locations of DOCCs 702 a-702 j. As described above, DOCCs 702 a-702 j may be configured such that the radial location of each DOCC overlaps less than 100% with the radial locations of its neighbor DOCCs in the radial plane. Additionally as described above with respect to FIGS. 7A and 7B, DOCCs 702 a-702 j may be increasingly disposed outward from rotational axis 704 of drill bit 701 such that DOCCs 702 a-702 j may be considered radially consecutive DOCCs going from DOCC 702 a to DOCC 702 j.

At step 1204, possible layouts of the first group of three radially consecutive DOCCs may be determined. For example, one of blades 726 a-726 e may be selected to have DOCC 702 a placed thereon. The blade may be selected such that DOCC 702 a may be placed at the radial location of DOCC 702 a determined in step 1202. In the present embodiment, blade 726 a may be selected for the placement of DOCC 702 a, however any other suitable blade 726 may also be selected. With DOCC 702 a placed on blade 726 a there are twelve different possibilities for placing each of DOCCs 702 b and 702 c on one of blades 726 b, 726 c, 726 d, and 726 e. However, of the twelve different possibilities, six may be selected to form a substantially force balanced group. The six force balanced possibilities with DOCC 702 a disposed on blade 726 a are listed below:

-   -   1. DOCC 702 a; Blade 726 a DOCC 702 b; Blade 726 b DOCC 702 c;         Blade 726 d     -   2. DOCC 702 a; Blade 726 a DOCC 702 b; Blade 726 c DOCC 702 c;         Blade 726 d     -   3. DOCC 702 a; Blade 726 a DOCC 702 b; Blade 726 c DOCC 702 c;         Blade 726 e     -   4. DOCC 702 a; Blade 726 a DOCC 702 b; Blade 726 d DOCC 702 c;         Blade 726 b     -   5. DOCC 702 a; Blade 726 a DOCC 702 b; Blade 726 d DOCC 702 c;         Blade 726 c     -   6. DOCC 702 a; Blade 726 a DOCC 702 b; Blade 726 e DOCC 702 c;         Blade 726 c         Similar possibilities may be determined with DOCC 702 a disposed         on one of blades 726 b-726 e.

At step 1206, one of the different possible configurations of disposing each of DOCCs 702 a-702 c on one of blades 726 a-726 e may be selected. For example, one of the configurations may be selected based on the relative symmetry of the placement of DOCCs 702 a-702 c on the face of drill bit 701 because DOCCs 702 a-702 c placed in a generally symmetrical manner may be substantially force balanced.

In the present example, configuration “3” listed above where DOCC 702 a may be disposed on blade 726 a, DOCC 702 b may be disposed on blade 726 c and DOCC 702 c may be disposed on blade 726 e is selected. At step 1208, the engineering tool may determine whether there are additional DOCCs to be disposed on blades 726 of drill bit 701. If there are additional DOCCs to be placed, method 1200 may proceed to step 1210. For example, after determining the disposition of DOCCs 702 a, 702 b, and 702 c on blades 726 a, 726 c and 726 e, respectively, it may be determined that DOCC 702 d is an additional DOCC that is to be disposed on a blade 726 of drill bit 701.

At step 1210, the disposition on one of blades 726 for the next consecutive DOCC in the radial plane may be selected. For example, DOCC 702 d may be the next radially consecutive DOCC after DOCC 702 c. The location for DOCC 702 d may be selected such that DOCCs 702 b, 702 c, and 702 d are a substantially forced balanced group of three radially consecutive DOCCs. Blades 726 c and 726 e may not be selected because they include DOCCs 702 b and 702 c, respectively. Blade 726 a may be possible, but DOCC 702 a may prevent the placement of DOCC 702 d at its desired radial location as determined in step 1202. That leaves blades 726 b and 726 d as potential locations for DOCC 702 d. In the present example, placement of DOCC 702 d on blade 726 b may result in a more symmetrical placement of DOCCs 702 b, 702 c, and 702 d on the face of drill bit 701 than placement of DOCC 702 d on blade 726 d. Therefore, DOCC 702 d may be disposed on blade 726 b to provide a generally symmetrical placement of DOCCs 702 b-702 d, which may reduce and/or minimize imbalance forces associated with DOCCs 702 b-702 d acting on drill bit 701.

Following step 1210, method 1200 may return to step 1208 to determine if there are any more DOCCs to be disposed on the drill bit. If no more DOCCs are to be disposed on the drill bit, method 1200 may proceed to step 1212. For example, steps 1208 and 1210 may be repeated with respect to drill bit 701 until the disposition of each of DOCCs 702 a-702 j on one of blades 726 a-726 e is determined and then method 1200 may proceed to step 1212.

At step 1212, a CDCCC may be determined for drill bit 701. Calculation of a CDCCC is described in detail below with respect to FIGS. 14 and 15 below. At step 1214, the engineering tool may help determine based on the CDCCC if DOCCs 702 a-702 j are in contact with the formation at substantially the same time. If one or more DOCCs are not in contact with the formation at substantially the same time, method 1200 may proceed to step 1216.

At step 1216, the axial position of one or more DOCCs may be adjusted based on the CDCCC. Such adjustment based on the CDCCC is described in further detail below with respect to FIGS. 14 and 15. Additionally, in some embodiments, the axial locations and surfaces of DOCCs 702 a-702 j may be adjusted such that DOCCs 702 a-702 j provide a substantially constant depth of cut control for the desired depth of cut as described in detail in PCT Application No. 2011/060184, filed Nov. 10, 2011 and titled “SYSTEM AND METHOD OF CONSTANT DEPTH OF CUT CONTROL OF DRILLING TOOLS” incorporated by reference herein.

Method 1200 may return to steps 1212 and 1214 following step 1216. Accordingly, the engineering tool may calculate the CDCCC again to determine if the DOCCs would be in contact with the formation at substantially the same time for the desired depth of cut. If the CDCCC indicates that the DOCCs would be in contact with the formation at substantially the same time for the desired depth of cut, method 1200 may end.

Accordingly, method 1200 may be used to reduce imbalance forces associated with DOCCs of a drill bit. Method 1200 may be used to reduce the imbalance forces by substantially balancing the groups of three radially consecutive DOCCs, adjusting the axial positions of the DOCCs or any combination thereof.

Modifications, additions or omissions may be made to method 1200 without departing from the scope of the present disclosure. For example, although method 1200 has been described with respect to drill bit 701 of FIGS. 7A and 7B, method 1200 may be used to force balance the radially consecutive groups of three DOCCs of any suitable drill bit. Additionally, in some embodiments, steps 1212 through 1216 may be omitted.

FIG. 13 illustrates an example method 1300 for disposing DOCCs on a drill bit such that the imbalance forces associated with the DOCCs acting on the drill bit may be reduced. Method 1300 may be used to dispose DOCCs on a drill bit such that each group of four radially consecutive DOCCs may be substantially force balanced. The steps of method 1300 may be performed by the “drilling engineering tool” or “engineering tool” described with respect to method 1200. For illustrative purposes, method 1300 is described with respect to drill bit 801 of FIGS. 8A and 8B; however, method 1300 may be performed with respect to any suitable drill bit.

Method 1300 may start, and at step 1302, the engineering tool may determine the desired radial locations of DOCCs 802 a-802 l. As described above, DOCCs 802 a-802 l may be configured such that the radial location of each DOCC overlaps less than 100% with the radial locations of its neighbor DOCCs in the radial plane. Additionally with respect to FIGS. 8A and 8B, DOCCs 802 a-802 l may be increasingly disposed outward from rotational axis 804 of drill bit 801 such that DOCCs 802 a-802 l may be considered radially consecutive DOCCs going from DOCC 802 a to DOCC 802 l.

At step 1304 possible layouts of the first group of four radially consecutive DOCCs may be determined. For example, one of blades 826 a-826 f may be selected to have DOCC 802 a placed thereon. The blade may be selected such that DOCC 802 a may be placed at the radial location of DOCC 802 a determined in step 1302. In the present embodiment blade 826 a may be selected for the placement of DOCC 802 a, however any other suitable blade 826 may also be selected. With DOCC 802 a placed on blade 826 a there are a multiple different possibilities for placing each of DOCCs 802 b, 802 c, and 802 d, on one of blades 826 b, 826 c, 826 d, 826 e, and 826 f, similarly to the availability of different placement possibilities of DOCCs 702 b and 702 c on one of blades 726 b, 726 c, 726 d, and 726 e described above.

At step 1306, one of the different possible configurations of disposing each of DOCCs 802 a-802 d on one of blades 826 a-826 f may be selected. For example, one of the configurations may be selected based on the relative symmetry of the placement of DOCCs 802 a-802 d on the face of drill bit 801 because DOCCs 802 a-802 d placed in a generally symmetrical manner may be substantially force balanced. In the present example, DOCC 802 a may be disposed on blade 826 a, DOCC 802 b may be disposed on blade 826 d, DOCC 802 c may be disposed on blade 826 c, and DOCC 802 d may be disposed on blade 826 f. At step 1308 it may be determined whether there are additional DOCCs to be disposed on one of blades 826 of drill bit 801. If there are additional DOCCs to be placed, method 1300 may proceed to step 1310. For example, after determining the disposition of DOCCs 802 a, 802 b, 802 c, and 802 d on blades 826 a, 826 d, 826 c, and 826 f, respectively, it may be determined that DOCC 802 e is an additional DOCC that is to be disposed on a blade of drill bit 801.

At step 1310 the disposition on one of blades 826 for the next consecutive DOCC in the radial plane may be selected. For example, DOCC 802 e may be the next radially consecutive DOCC after DOCC 802 d. The location for DOCC 802 e may be selected such that DOCCs 802 b, 802 c, 802 d, and 802 e are spaced in a generally symmetrical manner on the face of drill bit 801 such that DOCCs 802 b-802 e may be a substantially forced balanced group of four radially consecutive DOCCs. Blades 826 d, 826 c, and 826 f may not be selected because they include DOCCs 802 b, 802 c, and 802 d, respectively. Blade 826 a may be possible, but DOCC 802 a may prevent the placement of DOCC 802 e at its desired radial location as determined in step 1302. That leaves blades 826 b and 826 e as potential locations for DOCC 802 e. In the present example, placement of DOCC 802 e on blade 826 b may result in a more symmetrical placement of DOCCs 802 b-802 e on the face of drill bit 801 than placement of DOCC 802 e on blade 826 e. Therefore, DOCC 802 e may be disposed on blade 826 b to provide a generally symmetrical placement of DOCCs 802 b-802 e, which may reduce and/or minimize imbalance forces associated with DOCCs 802 b-802 e. Following step 1310 method 1300 may return to step 1308 to determine if there are any more DOCCs to be disposed on the drill bit. If no more DOCCs are to be disposed on the drill bit, method 1300 may proceed to step 1312. For example, steps 1308 and 1310 may be repeated with respect to drill bit 801 until the disposition of each of DOCCs 802 a-802 l on one of blades 826 a-826 f is determined and then method 1300 may proceed to step 1312.

At step 1312 a CDCCC may be determined for drill bit 801. Calculation of a CDCCC is described in detail below with respect to FIGS. 14 and 15. At step 1314, the engineering tool may help determine based on the CDCCC if DOCCs 802 a-802 l are in contact with the formation at substantially the same time for a desired depth of cut. If one or more DOCCs are not in contact with the formation at substantially the same time, method 1300 may proceed to step 1316.

At step 1316, the axial position of one or more DOCCs may be adjusted based on the CDCCC. Such adjustment based on the CDCCC is described in further detail below with respect to FIGS. 14 and 15. Additionally, in some embodiments, the axial locations and surfaces of DOCCs 802 a-802 l may be adjusted such that DOCCs 802 a-802 l provide a substantially constant depth of cut control for the desired depth of cut as described in detail in PCT Application No. 2011/060184, filed Nov. 10, 2011 and titled “SYSTEM AND METHOD OF CONSTANT DEPTH OF CUT CONTROL OF DRILLING TOOLS” incorporated by reference herein.

Method 1300 may return to steps 1312 and 1314 following step 1316. Accordingly, the engineering tool may calculate the CDCCC again to determine if the DOCCs would be in contact with the formation at substantially the same time for the desired depth of cut. If the CDCCC indicates that the DOCCs would be in contact with the formation at substantially the same time for the desired depth of cut, method 1300 may end.

Accordingly, method 1300 may be used to reduce imbalance forces associated with DOCCs of a drill bit. Method 1300 may be used to reduce the imbalance forces by substantially balancing the groups of four radially consecutive DOCCs, adjusting the axial positions of the DOCCs or any combination thereof.

Modifications, additions or omissions may be made to method 1300 without departing from the scope of the present disclosure. For example, although method 1300 has been described with respect to drill bit 801 of FIGS. 8A and 8B, method 1200 may be used to force balance the radially consecutive groups of four DOCCs of any suitable drill bit, such as drill bits 901, 1001, and 1101. Additionally, in some embodiments, steps 1312 through 1316 may be omitted.

As mentioned above, a critical depth of cut control curve may be determined such that the axial positions of DOCCs may be adjusted to improve the balance of a drill bit. FIG. 14A illustrates the face of a drill bit 1401 for which a critical depth of cut control curve (CDCCC) may be determined, in accordance with some embodiments of the present disclosure. FIG. 14B illustrates a bit face profile of drill bit 1401 of FIG. 14A.

Drill bit 1401 may include a plurality of blades 1426 that may include cutting elements 1428 and 1429. Additionally, blades 1426 b, 1426 d and 1426 f may include DOCC 1402 b, DOCC 1402 d and DOCC 1402 f, respectively, that may be configured to control the depth of cut of drill bit 1401. The critical depth of cut of drill bit 1401 may be determined for a radial location along drill bit 1401. For example, drill bit 1401 may include a radial coordinate R_(F) that may intersect with DOCC 1402 b at a control point P_(1402b), DOCC 1402 d at a control point P_(1402d,) and DOCC 1402 f at a control point P_(1402f). Additionally, radial coordinate R_(F) may intersect cutting elements 1428 a, 1428 b, 1428 c, and 1429 f at cutlet points 1430 a, 1430 b, 1430 c, and 1430 f, respectively, of the cutting edges of cutting elements 1428 a, 1428 b, 1428 c, and 1429 f, respectively.

The angular coordinates of control points P_(1402b), P_(1402d) and P_(1402f) (θ_(P1402b), θ_(P1402d) and θ_(P1402f), respectively) may be determined along with the angular coordinates of cutlet points 1430 a, 1430 b, 1430 c and 1430 f (θ_(1430a), θ_(1430b), θ_(1430c) and θ_(1430f), respectively). A depth of cut control provided by each of control points P_(1402b), P_(1402d) and P_(1402f) with respect to each of cutlet points 1430 a, 1430 b, 1430 c and 1430 f may be determined. The depth of cut control provided by each of control points P_(1402b), P_(1402d) and P_(1402f) may be based on the underexposure (δ_(1407i) depicted in FIG. 14B) of each of points P_(1402i) with respect to each of cutlet points 1430 and the angular coordinates of points P_(1402i) with respect to cutlet points 1430.

For example, the depth of cut of cutting element 1428 b at cutlet point 1430 b controlled by point P_(1402b) of DOCC 1402 b (Δ_(1430b)) may be determined using the angular coordinates of point P_(1402b) and cutlet point 1430 b (θ_(P1402b) and θ_(1430b), respectively), which are depicted in FIG. 14A. Additionally, Δ_(1430b) may be based on the axial underexposure (δ_(1407b)) of the axial coordinate of point P_(1402b) (Z_(P1402b)) with respect to the axial coordinate of intersection point 1430 b (Z_(1430b)), as depicted in FIG. 14B. In some embodiments, Δ_(1430b) may be determined using the following equations:

Δ_(1430b)=δ_(1407b)*360/(360−(θ_(P1402b)−θ_(1430b))); and

δ_(1407b) =Z _(1430b) −Z _(P1402b).

In the first of the above equations, θ_(P1402b) and θ_(1430b) may be expressed in degrees and “360” may represent a full rotation about the face of drill bit 1401. Therefore, in instances where θ_(P1402b) and θ_(1430b) are expressed in radians, the numbers “360” in the first of the above equations may be changed to “2π.” Further, in the above equation, the resultant angle of “(θ_(P1402b)−θ_(1430b))” (Δ_(θ)) may be defined as always being positive. Therefore, if resultant angle Δ_(θ) is negative, then Δ_(θ) may be made positive by adding 360 degrees (or 2π radians) to Δ_(θ). Similar equations may be used to determine the depth of cut of cutting elements 1428 a, 1428 c, and 1429 f as controlled by control point P_(1402b) at cutlet points 1430 a, 1430 c and 1430 f, respectively (Δ_(1430a), Δ_(1430c) and Δ_(1430f), respectively).

The critical depth of cut provided by point P_(1402b) (Δ_(P1402b)) may be the maximum of Δ_(1430a), Δ_(1430b), Δ_(1430c) and Δ_(1430f) and may be expressed by the following equation:

Δ_(P1402b)=max[Δ_(1430a),Δ_(1430b),Δ_(1430c),Δ_(1430f)].

The critical depth of cut provided by points P_(1402d) and P_(1402f) (Δ_(P1402d) and Δ_(P1402f), respectively) at radial coordinate R_(F) may be similarly determined. The overall critical depth of cut of drill bit 1401 at radial coordinate R_(F) (Δ_(RE)) may be based on the minimum of Δ_(P1402b), Δ_(P1402d) and Δ_(P1402f) and may be expressed by the following equation:

Δ_(RF)=min[Δ_(P1402b),Δ_(P1402d),Δ_(P1402d)].

Accordingly, the overall critical depth of cut of drill bit 1401 at radial coordinate R_(F) (Δ_(RF)) may be determined based on the points where DOCCs 1402 and cutting elements 1428/1429 intersect R_(F). Although not expressly shown here, it is understood that the overall critical depth of cut of drill bit 1401 at radial coordinate R_(F) (Δ_(RE)) may also be affected by control points P_(1426i) (not expressly shown in FIGS. 14A and 14B) that may be associated with blades 1426 configured to control the depth of cut of drill bit 1401 at radial coordinate R_(F). In such instances, a critical depth of cut provided by each control point P_(1426i) (Δ_(P1426i)) may be determined. Each critical depth of cut Δ_(P1426i) for each control point P_(1426i) may be included with critical depth of cuts Δ_(P1402i) in determining the minimum critical depth of cut at R_(F) to calculate the overall critical depth of cut Δ_(RF) at radial location R_(F).

To determine a critical depth of cut control curve of drill bit 1401, the overall critical depth of cut at a series of radial locations R_(f) (Δ_(Rf)) anywhere from the center of drill bit 1401 to the edge of drill bit 1401 may be determined to generate a curve that represents the critical depth of cut as a function of the radius of drill bit 1401. In the illustrated embodiment, DOCCs 1402 b, 1402 d, and 1402 f may be configured to control the depth of cut of drill bit 1401 for a radial swath 1408 defined as being located between a first radial coordinate R_(A) and a second radial coordinate R_(B). Accordingly, the overall critical depth of cut may be determined for a series of radial coordinates R_(f) that are within radial swath 1408 and located between R_(A) and R_(B), as disclosed above. Once the overall critical depths of cuts for a sufficient number of radial coordinates R_(f) are determined, the overall critical depth of cut may be graphed as a function of the radial coordinates R_(f). FIGS. 14C and 14D illustrate critical depth of cut control curves where the critical depth of cut is plotted as a function of the bit radius, in accordance with some embodiments of the present disclosure.

The critical depth of cut control curve may be used to determine the minimum critical depth of cut control as provided by the DOCCs and/or blades of a drill bit. Additionally, as mentioned above, the CDCCC may be used to determine if DOCCs are in contact with a formation at substantially the same time for a desired depth of cut. For example, FIGS. 14C and 14D both illustrate a critical depth of cut control curve for drill bit 1401 between radial coordinates R_(A) and R_(B). The z-axis in FIGS. 14C and 14D may represent the critical depth of cut per revolution (in/rev) along the rotational axis of drill bit 1401, and the radial (R) axis may represent the radial distance from the rotational axis of drill bit 1401.

FIG. 14C illustrates a critical depth of cut control curve where the axial positions of one or more of DOCCs 1402 of drill bit 1401 have not yet been configured by using the CDCCC. As shown in FIG. 14C the minimum critical depth of cut provided by DOCCs 1402 may not be the same or even. Accordingly, DOCCs 1402 may not be in contact with the formation at substantially the same time. Additionally, in the illustrated embodiment, the desired minimum critical depth of cut for each DOCC 1402 may be 0.3 inches/revolution (in/rev). However, FIG. 14C indicates that only one of the three DOCCs 1402 may be substantially close to providing a minimum critical depth of cut of 0.3 in/rev. Accordingly, the critical depth of cut control curve of FIG. 14C indicates that a modification may be made to DOCCs 1402 such that the minimum critical depth of cut provided by each of DOCCs 1402 may be substantially equal and such that DOCCs 1402 may be in contact with the formation at substantially the same time.

For example, as shown in FIG. 14A, DOCC 1402 f may be radially located closest to the rotational axis of drill bit 1401 with respect to DOCCs 1402 b and 1402 d, DOCC 1402 d may be radially located furthest from the rotational axis of drill bit 1401 with respect to DOCC 1402 b and DOCC 1402 f, and DOCC 1402 b may be radially located between the radial locations of DOCCs 1402 f and 1402 d. Accordingly, the lowest point on the bump closest to the z-axis of the CDCCC in FIG. 14C may indicate the minimum depth of cut control provided by DOCC 1402 f, the lowest point on the middle bump of the CDCCC may indicate the minimum critical depth of cut as provided by DOCC 1402 b, and the lowest point on the bump furthest from the z-axis of the CDCCC may indicate the minimum depth of cut control provided by DOCC 1402 d.

As mentioned above, in the current embodiment, the desired minimum depth of cut control provided by each of DOCCs 1402 may be 0.3 in/rev. Therefore, based on the CDCCC of FIG. 14C, the axial position of DOCCs 1402 b and 1402 d may be adjusted such that DOCCs 1402 b and 1402 d may provide the desired minimum critical depth of cut of 0.3 in/rev. After adjusting the axial positions of DOCCs 1402 b and 1402 d, the CDCCC may be calculated again to determine whether DOCCs 1402 b and 1402 d have minimum critical depths of cut that may be substantially equal to the desired minimum depth of cut of 0.3 in/rev. The process may be repeated as many times as necessary to achieve the desired result. FIG. 14D illustrates a CDCCC where DOCCs 1402 b, 1402 d and 1402 f of drill bit 1401 have been adjusted accordingly such that each of DOCCs 1402 b, 1402 d, and 1402 f have a minimum critical depth of cut that is substantially equal to the desired minimum depth of cut of 0.3 in/rev of this particular embodiment.

FIG. 14D illustrates that by analyzing a CDCCC and adjusting the axial position of one or more DOCCs 1402, the minimum critical depths of cut provided by each of DOCCs 1402 may be substantially equal. Additionally, such adjustments may result in each DOCC 1402 substantially providing a desired minimum critical depth of cut. Further, such adjustments may allow for DOCCs 1402 to be in contact with the formation at substantially the same time to reduce imbalance forces and vibrations.

Modifications, additions or omissions may be made to FIGS. 14A-14D without departing from the scope of the present disclosure. For example, as discussed above, blades 1426, DOCCs 1402 or any combination thereof may affect the critical depth of cut at one or more radial coordinates and the CDCCC may be determined accordingly. Further, the above description of the CDCCC calculation may be used to determine a CDCCC of any suitable drill bit such as drill bits 401, 501, 601, 701, 801, 901, 1001, and 1101 detailed above.

FIG. 15 illustrates an example method 1500 of determining and generating a CDCCC in accordance with some embodiments of the present disclosure. The steps of method 1500 may be performed by the “drilling engineering tool” or “engineering tool” described above with respect to methods 1200 and 1300.

In the illustrated embodiment, the cutting structures of the drill bit, including at least the locations and orientations of all cutting elements and DOCCs, may have been previously designed. However in other embodiments, method 1500 may include steps for designing the cutting structure of the drill bit. For illustrative purposes, method 1500 is described with respect to drill bit 1401 of FIGS. 14A-14D; however, method 1500 may be used to determine the CDCCC of any suitable drill bit.

Method 1500 may start, and at step 1502, the engineering tool may select a radial swath of drill bit 1401 for analyzing the critical depth of cut within the selected radial swath. In some instances the selected radial swath may include the entire face of drill bit 1401 and in other instances the selected radial swath may be a portion of the face of drill bit 1401. For example, the engineering tool may select radial swath 1408 as defined between radial coordinates R_(A) and R_(B) and controlled by DOCCs 1402 b, 1402 d and 1402 f, shown in FIGS. 14A-14D.

At step 1504, the engineering tool may divide the selected radial swath (e.g., radial swath 1408) into a number, Nb, of radial coordinates (R_(f)) such as radial coordinate R_(F) described in FIGS. 14A and 14B. For example, radial swath 1408 may be divided into nine radial coordinates such that Nb for radial swath 1408 may be equal to nine. The variable “f” may represent a number from one to Nb for each radial coordinate within the radial swath. For example, “R₁” may represent the radial coordinate of the inside edge of a radial swath. Accordingly, for radial swath 1408, “R₁” may be approximately equal to R_(A). As a further example, “R_(Nb)” may represent the radial coordinate of the outside edge of a radial swath. Therefore, for radial swath 1408, “R_(Nb)” may be approximately equal to R_(B).

At step 1506, the engineering tool may select a radial coordinate R_(f) and may identify control points (P_(i)) located at the selected radial coordinate R_(f) and associated with a DOCC and/or blade. For example, the engineering tool may select radial coordinate R_(F) and may identify control points P_(1402i) and P_(1426i) associated with DOCCs 1402 and/or blades 1426 and located at radial coordinate R_(F), as described above with respect to FIGS. 14A and 14B.

At step 1508, for the radial coordinate R_(f) selected in step 1506, the engineering tool may identify cutlet points (C_(j)) each located at the selected radial coordinate R_(f) and associated with the cutting edges of cutting elements. For example, the engineering tool may identify cutlet points 1430 a, 1430 b, 1430 c and 1430 f located at radial coordinate R_(F) and associated with the cutting edges of cutting elements 1428 a, 1428 b, 1428 c, and 1429 f, respectively, as described and shown with respect to FIGS. 14A and 14B.

At step 1510 the engineering tool may select a control point P_(i) and may calculate a depth of cut for each cutlet C_(j), as controlled by the selected control point P_(i) (θ_(Cj)), as described above with respect to FIGS. 14A and 14B. For example, the engineering tool may determine the depth of cut of cutlets 1430 a, 1430 b, 1430 c, and 1430 f as controlled by control point P_(1402b) (Δ_(1430a), Δ_(1430b), Δ_(1430c), and Δ_(1430f), respectively) by using the following equations:

Δ_(1430a)=δ_(1407a)*360/(360−(θ_(P1402b)−θ_(1430a)));

δ_(1407a) =Z _(1430a) −Z _(P1402b);

Δ_(1430b)=δ_(1407b)*360/(360−(θ_(P1402b)−θ_(1430b)));

δ_(1407b) =Z _(1430b) −Z _(P1402b);

Δ_(1430c)=δ_(1407c)*360/(360−(θ_(P1402b)−θ_(1430c)));

δ_(1407c) =Z _(1430c) −Z _(P1402b);

Δ_(1430f)=δ_(1407f)*360/(360−(θ_(P1402b)−θ_(1430f))); and

δ_(1407f) =Z _(1430f) −Z _(P1402b).

At step 1512, the engineering tool may calculate the critical depth of cut provided by the selected control point (Δ_(Pi)) by determining the maximum value of the depths of cut of the cutlets C_(j) as controlled by the selected control point P_(i) (Δ_(Cj)) and calculated in step 1510. This determination may be expressed by the following equation:

Δ_(Pi)=max{Δ_(Cj)}.

For example, control point P_(1402b) may be selected in step 1510 and the depths of cut for cutlets 1430 a, 1430 b, 1430 c, and 1430 f as controlled by control point P_(1402b) (Δ_(1430a), Δ_(1430b), Δ_(1430c), and Δ_(1430f), respectively) may also be determined in step 1510, as shown above. Accordingly, the critical depth of cut provided by control point P_(1402b) (Δ_(P1402b)) may be calculated at step 1512 using the following equation:

Δ_(P1402b)=max[Δ_(1430a),Δ_(1430b),Δ_(1430c),Δ_(1430f)].

The engineering tool may repeat steps 1510 and 1512 for all of the control points P_(i) identified in step 1506 to determine the critical depth of cut provided by all control points P_(i) located at radial coordinate R_(f). For example, the engineering tool may perform steps 1510 and 1512 with respect to control points P_(1402d) and P_(1402f) to determine the critical depth of cut provided by control points P_(1402d) and P_(1402f) with respect to cutlets 1430 a, 1430 b, 1430 c, and 1430 f at radial coordinate R_(F) shown in FIGS. 14A and 14B (e.g., Δ_(P1402d) and Δ_(P1402f), respectively).

At step 1514, the engineering tool may calculate an overall critical depth of cut at the radial coordinate R_(f) (Δ_(Rf)) selected in step 1506. The engineering tool may calculate the overall critical depth of cut at the selected radial coordinate R_(f) (Δ_(Rf)) by determining a minimum value of the critical depths of cut of control points P_(i) (Δ_(Pi)) determined in steps 1510 and 1512. This determination may be expressed by the following equation:

Δ_(Rf)=min{Δ_(Pi)}.

For example, the engineering tool may determine the overall critical depth of cut at radial coordinate R_(F) of FIGS. 14A and 14B by using the following equation:

Δ_(RF)=min[Δ_(P1402b),Δ_(P1402d),Δ_(P1402f)].

The engineering tool may repeat steps 1506 through 1514 to determine the overall critical depth of cut at all the radial coordinates R_(f) generated at step 1504.

At step 1516, the engineering tool may plot the overall critical depth of cut (Δ_(Rf)) for each radial coordinate R_(f), as a function of each radial coordinate R_(f). Accordingly, a critical depth of cut control curve may be calculated and plotted for the radial swath associated with the radial coordinates R_(f). For example, the engineering tool may plot the overall critical depth of cut for each radial coordinate R_(f) located within radial swath 1408, such that the critical depth of cut control curve for swath 1408 may be determined and plotted, as depicted in FIGS. 14C and 14D. Following step 1516, method 1500 may end.

Accordingly, method 1500 may be used to calculate and plot a critical depth of cut control curve of a drill bit. The critical depth of cut control curve may be used to determine whether the drill bit provides a substantially even control of the depth of cut of the drill bit and whether DOCCs may be in contact with the formation being drilled at substantially the same time. Therefore, the critical depth of cut control curve may be used to modify the DOCCs of the drill bit configured to control the depth of cut of the drill bit to improve the efficiency and balance of the DOCCs.

Modifications, additions, or omissions may be made to method 1500 without departing from the scope of the present disclosure. For example, the order of the steps may be performed in a different manner than that described and some steps may be performed at the same time. Additionally, each individual step may include additional steps without departing from the scope of the present disclosure. Further, although method 1500 is described with respect to drill bit 1401, method 1500 may be used to calculate the CDCCC of any suitable drill bit including drill bits 401, 501, 601, 701, 801, 901, 1001, and 1101 described above.

Although the present disclosure has been described with several embodiments, various changes and modifications may be suggested to one skilled in the art. For example, although the present disclosure describes the configurations of DOCCs with respect to drill bits having specific blade configurations, the same principles may be used to reduce the imbalance forces of any suitable drilling tool according to the present disclosure. It is intended that the present disclosure encompasses such changes and modifications as fall within the scope of the appended claims. 

What is claimed is:
 1. A method for configuring a drill bit comprising: determining a number of blades of a drill bit; if the number of blades of the drill bit equals five, disposing each of a plurality of depth of cut controllers (DOCCs) on one of the blades of the drill bit such that each group of three radially consecutive DOCCs of the plurality of DOCCs is substantially force balanced; and if the number of blades of the drill bit is greater than five, disposing each of the plurality of DOCCs on one of the blades of the drill bit such that each group of four radially consecutive DOCCs of the plurality of DOCCs is substantially force balanced.
 2. The method of claim 1, further comprising adjusting an axial position of at least one of the plurality of DOCCs such that the plurality of DOCCs are in contact with a formation to be drilled at substantially the same time.
 3. The method of claim 2, further comprising adjusting the axial position of the at least one DOCC based on a critical depth of cut control curve.
 4. The method of claim 1, further comprising: determining a desired radial position for each of the plurality of DOCCs; and disposing each of the plurality of DOCCs on one of the blades based on the desired radial position of the respective DOCC.
 5. The method of claim 4, further comprising determining the desired radial position for each of the plurality of DOCCs such that the desired radial position of each of the plurality of DOCCs at least partially overlaps the desired radial position of its respective neighbor DOCC in a radial plane.
 6. The method of claim 1, further comprising disposing each of the plurality of DOCCs on one of the blades such that each DOCC of each group of three radially consecutive DOCCs is generally spaced symmetrically from the other DOCCs of the respective group on a face of the drill bit.
 7. The method of claim 1, further comprising disposing each of the plurality of DOCCs on one of the blades such that each DOCC of each group of four radially consecutive DOCCs is generally spaced symmetrically from the other DOCCs of the respective group on a face of the drill bit.
 8. The method of claim 1, further comprising disposing each of the plurality of DOCCs on one of the blades such that each DOCC of each group of three radially consecutive DOCCs is spaced from the other DOCCs of the respective group by between approximately 100 degrees and 140 degrees with respect to a rotational axis of the drill bit.
 9. The method of claim 1, further comprising disposing each of the plurality of DOCCs on one of the blades such that each DOCC of each group of four radially consecutive DOCCs is spaced from the other DOCCs of the respective group by between approximately 75 degrees and 105 degrees with respect to a rotational axis of the drill bit.
 10. The method of claim 1, wherein if the number of blades of the drill bit is five, the method further comprises: disposing each DOCC of a first group of three radially consecutive DOCCs on one of the blades such that the first group is substantially force balanced, the first group of three radially consecutive DOCCs including a first DOCC, a second DOCC neighboring the first DOCC in a radial plane, and a third DOCC neighboring the second DOCC in the radial plane; and disposing a fourth DOCC on one of the blades such that a second group of three radially consecutive DOCCs is substantially force balanced, the fourth DOCC neighboring the third DOCC in the radial plane, and the second group of three radially consecutive DOCCs including the second DOCC, the third DOCC, and the fourth DOCC.
 11. The method of claim 1, wherein if the number of blades of the drill bit is greater than five, the method further comprises: disposing each DOCC of a first group of four radially consecutive DOCCs on one of the blades such that the first group is substantially force balanced, the first group of four radially consecutive DOCCs including a first DOCC, a second DOCC neighboring the first DOCC in a radial plane, a third DOCC neighboring the second DOCC in the radial plan, and a fourth DOCC neighboring the third DOCC in the radial plane; and disposing a fifth DOCC on one of the blades such that a second group of four radially consecutive DOCCs is substantially force balanced, the fifth DOCC neighboring the fourth DOCC in the radial plane and the second group of four radially consecutive DOCCs including the second DOCC, the third DOCC, the fourth DOCC, and the fifth DOCC.
 12. A drill bit comprising: a bit body including a rotational axis extending therethrough; five blades disposed on the bit body that form a bit face; a plurality of cutting elements each disposed on one of the blades; and a plurality of depth of cut controllers (DOCCs) configured to control a depth of cut of at least one of the cutting elements, each of the plurality of DOCCs disposed on one of the blades such that each group of three radially consecutive DOCCs of the plurality of DOCCs is substantially force balanced.
 13. The drill bit of claim 12, wherein each DOCC of the plurality of DOCCs has an axial position such that the plurality of DOCCs are in contact with a formation to be drilled at substantially the same time.
 14. The drill bit of claim 13, wherein the axial position of the plurality of DOCCs is based on a critical depth of cut control curve.
 15. The drill bit of claim 12, wherein each DOCC of the plurality of DOCCs has a desired radial position and each of the plurality of DOCCs is disposed on one of the blades based on the desired radial position of the respective DOCC.
 16. The drill bit of claim 15, wherein the desired radial position for each of the plurality of DOCCs is such that the desired radial position of each of the plurality of DOCCs at least partially overlaps the desired radial position of its respective neighbor DOCC in a radial plane.
 17. The drill bit of claim 12, wherein each of the plurality of DOCCs is disposed on one of the blades such that each DOCC of each group of three radially consecutive DOCCs is generally spaced symmetrically from the other DOCCs of the respective group on a face of the drill bit.
 18. The drill bit of claim 12, wherein each of the plurality of DOCCs is disposed on one of the blades such that each DOCC of each group of three radially consecutive DOCCs is spaced from the other DOCCs of the respective group by between approximately 100 degrees and 140 degrees with respect to the rotational axis of the drill bit.
 19. A drill bit comprising: a bit body including a rotational axis extending therethrough; more than five blades disposed on the bit body to form a bit face; a plurality of cutting elements each disposed on one of the blades; and a plurality of depth of cut controllers (DOCCs) configured to control a depth of cut of at least one of the cutting elements, each of the plurality of DOCCS disposed on one of the blades such that each group of four radially consecutive DOCCs of the plurality of DOCCs is substantially force balanced.
 20. The drill bit of claim 19, wherein each DOCC of the plurality of DOCCs has an axial position such that the plurality of DOCCs are in contact with a formation to be drilled at substantially the same time.
 21. The drill bit of claim 20, wherein the axial position of the plurality of DOCCs is based on a critical depth of cut control curve.
 22. The drill bit of claim 19, wherein each DOCC of the plurality of DOCCs has a desired radial position and each of the plurality of DOCCs is disposed on one of the blades based on the desired radial position of the respective DOCC.
 23. The drill bit of claim 22, wherein the desired radial position for each of the plurality of DOCCs is such that the desired radial position of each of the plurality of DOCCs at least partially overlaps the desired radial position of its respective neighbor DOCC in a radial plane.
 24. The drill bit of claim 19, wherein each of the plurality of DOCCs is disposed on one of the blades such that each DOCC of each group of four radially consecutive DOCCs is generally spaced symmetrically from the other DOCCs of the respective group on a face of the drill bit.
 25. The drill bit of claim 19, wherein each of the plurality of DOCCs is disposed on one of the blades such that each DOCC of each group of four radially consecutive DOCCs is spaced from the other DOCCs of the respective group by between approximately 75 degrees and 105 degrees with respect to the rotational axis of the drill bit. 